2
votes
2answers
516 views

Can this informal argument (for the fact that almost all reals in the unit interval are irrational) be saved?

In the textbook from which I am teaching a Discrete Math course, the authors propose randomly generating an infinite sequence of decimal digits $d_1, d_2, \dots$. We are to think of this as the ...
6
votes
2answers
912 views

Good examples of random variables whose image is not a measurable set?

Are their simple/natural examples of real-valued Borel-measurable random variables whose image is not a Borel set? Something that occurs "naturally"? I am teaching Doob's lemma (for two real-valued ...
7
votes
4answers
798 views

Characterization of the Poisson law

This semester, I teach an introduction to probability course tailored for students with no science background and so with very very little prerequisites. We started with the basics of analytic ...
1
vote
2answers
5k views

Examples of random variables

I'm looking for a list of examples of random variables to use in teaching a measure-theoretic probability course. For example, the Rademacher functions are an explicit construction of independent ...